Related papers: Partition Function Zeros for Aperiodic Systems
In quantum dynamics, the Loschmidt amplitude is analogous to the partition function in the canonical ensemble. Zeros in the partition function indicate a phase transition, while the presence of zeros in the Loschmidt amplitude indicates a…
We investigate the Ising model on a spherical surface, utilizing a Fibonacci lattice to approximate uniform coverage. This setup poses challenges in achieving consistent lattice distribution across the sphere for comparison with planar…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
The mixed spin-(1/2,1) Ising chain with axial and rhombic zero-field splitting parameters in a presence of the longitudinal magnetic field is exactly solved within the framework of decoration-iteration transformation and transfer-matrix…
This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and…
We study in detail the zero set of a regular function of a quaternionic or octonionic variable. By means of a division lemma for convergent power series, we find the exact relation existing between the zeros of two octonionic regular…
A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic…
We consider the problem of computing the partition function $\sum_x e^{f(x)}$, where $f: \{-1, 1\}^n \longrightarrow {\Bbb R}$ is a quadratic or cubic polynomial on the Boolean cube $\{-1, 1\}^n$. In the case of a quadratic polynomial $f$,…
We study the partition function and free energy of the Curie-Weiss model with complex temperature, and partially describe its phase transitions. As a consequence, we obtain information on the locations of zeros of the partition function.
We study the zero-temperature criticality of the Ising model on two-dimensional dynamical triangulations to contemplate its physics. As it turns out, an inhomogeneous nature of the system yields an interesting phase diagram and the physics…
We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the special boundary conditions that are obtained from…
We discuss the implications of studies of partition function zeros and equimodular curves for the analytic properties of the Ising model on a square lattice in a magnetic field. In particular we consider the dense set of singularities in…
We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the…
We study the Yang-Lee zeros of a random matrix partition function with the global symmetries of the QCD partition function. We consider both zeros in the complex chemical potential plane and in the complex mass plane. In both cases we find…
In the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of any planar analytic Hamiltonian system. We apply it to several…
We study dimensional crossover in Ising systems at complex temperatures by comparing three types of system: the infinite isotropic 2D Ising model; the infinite anisotropic 2D Ising model; and Ising ladders with a finite number of legs. In…
We investigate the thermodynamics of a combined Dicke- and Ising-model which exhibits a rich phenomenology arising from the second order and quantum phase transitions from the respective models. The partition function is calculated using…